Question 1

How do you convert a percent to a fraction?

Accepted Answer

To convert a percent to fraction: 1) Write the percent as a fraction with denominator 100. 2) Simplify the fraction by dividing both numerator and denominator by their greatest common divisor (GCD). Formula: Percent → Percent/100 → Simplified fraction. Example: 75% = 75/100 = 3/4 (divided by 25). The % symbol means 'out of 100', so any percent can be written as a fraction over 100.

Question 2

What is 50% as a fraction?

Accepted Answer

50% as a fraction is 1/2. To calculate: 50% = 50/100, then simplify by dividing both by 50 (the GCD) to get 1/2. This means 50% represents one half, or exactly half of the whole. It's one of the most common percentage-to-fraction conversions and appears frequently in everyday life, from sale discounts to probability calculations.

Question 3

How to convert 25% to a fraction?

Accepted Answer

To convert 25% to fraction: Step 1: Write as 25/100. Step 2: Find GCD of 25 and 100, which is 25. Step 3: Divide both numerator and denominator by 25. Step 4: 25÷25 = 1 and 100÷25 = 4. Therefore, 25% = 1/4. This fraction represents one quarter, which is commonly used in measurements, cooking, and financial calculations.

Question 4

What is the formula for percent to fraction conversion?

Accepted Answer

The formula for converting percents to fractions is: Fraction = Percent/100, then simplify. Where you place the percent number over 100, then reduce to lowest terms by dividing both numerator and denominator by their GCD. For decimal percents like 12.5%, first eliminate decimals: 12.5/100 = 125/1000, then simplify to 1/8. Always simplify for the final answer unless instructed otherwise.

Question 5

How do you convert decimal percentages to fractions?

Accepted Answer

For decimal percentages (like 12.5% or 33.33%): Step 1: Write as decimal/100. Example: 12.5/100. Step 2: Multiply numerator and denominator by 10, 100, etc. to remove decimals. Example: 125/1000. Step 3: Simplify. Example: 125/1000 = 1/8 (divide by 125). For 33.33%: Write as 33.33/100 = 3333/10000 ≈ 1/3. Repeating decimals often indicate common fractions.

Question 6

What are common percent to fraction conversions?

Accepted Answer

Common percent to fraction conversions include: 10% = 1/10, 20% = 1/5, 25% = 1/4, 33.33% = 1/3, 40% = 2/5, 50% = 1/2, 60% = 3/5, 66.67% = 2/3, 75% = 3/4, 80% = 4/5, 90% = 9/10, 100% = 1, 125% = 5/4, 150% = 3/2, 200% = 2. Memorizing these helps with quick mental calculations and estimation in everyday situations.

Question 7

How to convert percents greater than 100% to fractions?

Accepted Answer

Percents greater than 100% convert to improper fractions (numerator > denominator): Use the same method: Percent/100, then simplify. Example: 150% = 150/100 = 3/2 (divide by 50). You can also convert to mixed numbers: 150% = 3/2 = 1 1/2. Another example: 250% = 250/100 = 5/2 = 2 1/2. Percents over 100% represent more than one whole and are common in growth rates and comparisons.

Question 8

Why do we divide by 100 when converting percent to fraction?

Accepted Answer

We divide by 100 when converting percent to fraction because 'percent' literally means 'per hundred' or 'out of 100'. The % symbol represents division by 100. So 75% means '75 per hundred' or 75/100. This is why the first step is always to write the percent number over 100. After creating this fraction, we simplify it to get the final answer in lowest terms.

Question 9

How do you simplify fractions when converting from percents?

Accepted Answer

To simplify fractions from percents: 1) Find the GCD (Greatest Common Divisor) of numerator and denominator. 2) Divide both by the GCD. Example: 80% = 80/100. GCD(80, 100) = 20. Divide both: 80÷20 = 4, 100÷20 = 5. Result: 4/5. Quick GCD method: List factors of both numbers and find the largest common factor. Or use the Euclidean algorithm for large numbers. Always simplify to lowest terms for the final answer.

Question 10

Can you convert percent to fraction without a calculator?

Accepted Answer

Yes, you can convert percent to fraction without a calculator: Method 1: Write as fraction over 100 and simplify mentally. Example: 50% = 50/100 = 1/2. Method 2: Recognize common conversions (25%=1/4, 50%=1/2, 75%=3/4). Method 3: For percents ending in 0 or 5, simplification is easier. Example: 20% = 20/100 = 1/5. With practice, you can quickly convert many common percents mentally by recognizing patterns and using multiplication facts.

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